Tuesday, May 5, 14:00, 7.527
Daniel Juteau (Caen)
(Generalized, modular) Springer correspondence I, II.
In a first part, I will explain the main ideas of the Springer
correspondence, which relates irreducible representations of a Weyl group to
the geometry of the nilpotent cone in the associated Lie algebra, and some
idea of a modular version which I did in my thesis several years ago.
In the second part, I will talk about joint work with P. Achar, A. Henderson
and S. Riche where we study a modular analogue of Lusztig's generalization
of Springer correspondence. There are induction and restriction functors for
perverse sheaves on nilpotent cones, and a notion of cuspidality, like in
Harish-Chandra theory. Each cuspidal sheaf on a Levi subgroup gives rise to
an induction series, which is parametrized by irreducible representations of
a "relative Weyl group". I will say what we know about the classification of
cuspidal objects, which is very close to the one for modular representations
of finite reductive groups.